since, the lines x+y=6 and x+2y=4 are two diameters of the circle, then their point of intersection will be the centre of circle. Put y=6−x in x+2y=4, we get x+2(6−x)=4 ⇒x+12−2x=4 ⇒−x=−8 ⇒x=8 ⇒y=6−8=−2 Hence, centre of the circle is (8,−2) . Radius of circle = Distance between (8,−2) and (6,2) =√(8−6)2+(−2−2)2 =√4+16=√20=2√5